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I have had teaching responsibilities since I began graduate school. At SUNY at Buffalo, I was an assistant for courses in calculus of a single variable, multivariable calculus, and linear algebra; at SUNY at

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Having taught calculus for years, I understand that most students' struggles with the course are in algebra. Evaluating limits, derivatives, and definite integrals require some algebraic manipulation, knowledge of algebraic identities and trigonometric identities, and familiarity with inequalities. Studying calculus is also a review of algebra.

I am a graduate student at Binghamton University. I have taught both Calculus I and Calculus II here. I have also tutored students in these courses as well as multidimensional Calculus. I have numerous sample tests to give students.

I am a graduate student and have taken a course in discrete math (combinatorics). Taking algebra and analysis courses also has exposed me to application of discrete math. So, I have had plenty of exposure to the subject. I have also tutored several students in discrete math.

There are many counting techniques in discrete math. A permutation of letters is any arrangement of them in a row. The rule to calculate the number of permutations in "number" is similar but different than the rule to calculate the number of permutations in "repetition." The difference is that the letters in "number" are distinct and the letters "e," "i," and "t" are repeated in "repetition."

A combination is a selection of objects from a set of objects. The rule to calculate the number of straights in poker is different than the rule to calculate the coefficient of x^{2}yz^{3} in the expansion of (x + y + z)^{6}. The difference is that calculating the number of straights is a combination without repetition and calculating the coefficient of x^{2}yz^{3} is a combination with repetition.

There are many, many binomial identities. These identities give nice formulas. For example, the Parallel Summation Identity may be used to give the rule for adding the squares of the first n positive integers and for adding the cubes of the first n positive integers.

I can calculate the number of combinations of two-pair poker hands, the number of ways to order ten single-scoop ice cream cones from 31 flavors, and the number of nonnegative, integral solutions to x_{1} + x_{2} + x_{3} + x_{4} = 15. I know how to apply these counting techniques to the Binomial Theorem and the Multinomial Theorem.

I have taught this class at Binghamton University. The course began with solving systems of linear equations. The translation of a system of linear equations to a matrix equation and the matrix operations that made two matrix equations equivalent were next discussed. I know the many equivalent conditions for a square matrix to be invertible.

I know about vector spaces, and equivalent definitions of subspaces. Matrices are used to define linear transformations. The kernel and range of linear transformations are subspace of Euclidean space.

A dot product is defined on Euclidean space. With the dot product, orthogonal vectors can be defined. The Gram-Schmidt Process defines an orthogonal (and orthonormal) basis for a subspace of Euclidean space. With the dot product, a notion of distance is defined on Euclidean space. Using this notion of distance, the line of best fit can be defined.

Trigonometry is the study of the relationships between arcs of a circle and the ratio of sides of right triangles. It was originally studied in ancient Egypt for astronomy and geography. It is needed to properly learn calculus, physics, and engineering.

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